I was able to numerically "show" that an M/M/n queue is concave increasing in the number for $n$ servers, which makes intuitive sense. However is there a formal analytical proof for it? Where can I find it?
Dyer and Proll (1977)1 showed that for an M/M/c queue, the mean waiting time is a strictly decreasing and convex function of c.
 Dyer, M. E., Proll, L. G. (1977). On the Validity of Marginal Analysis for Allocating Servers in M/M/c Queues. Management Science. 23(9):1019-1022.